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MATLAB(R) releases over the last 3 years have witnessed a continuing growth in the dynamic modeling capabilities offered by the System Identification Toolbox(TM). The emphasis has been on integrating deep learning architectures and training…
The goal of this article is to study fundamental mechanisms behind so-called indirect and direct data-driven control for unknown systems. Specifically, we consider policy iteration applied to the linear quadratic regulator problem. Two…
Branch prediction is an architectural feature that speeds up the execution of branch instruction on pipeline processors and reduces the cost of branching. Recent advancements of Deep Learning (DL) in the post Moore's Law era is accelerating…
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…
The ubiquitous backpropagation algorithm requires sequential updates through the network introducing a locking problem. In addition, back-propagation relies on the transpose of forward weight matrices to compute updates, introducing a…
We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
Deep learning has made significant applications in the field of data science and natural science. Some studies have linked deep neural networks to dynamic systems, but the network structure is restricted to the residual network. It is known…
We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to…
A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…
The development of the back-propagation algorithm represents a landmark in neural networks. We provide an approach that conducts the back-propagation again to reverse the traditional back-propagation process to optimize the input loss at…
The integration of Deep Learning (DL) in System Dynamics (SD) modeling for transportation logistics offers significant advantages in scalability and predictive accuracy. However, these gains are often offset by the loss of explainability…
In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…
We describe an approach for estimating the statistical risk of deep networks that contain a mix of learned and known operators. Building on the maximal training error bounds previously established for known operator learning, we derive a…
We review several of the most widely used techniques for training recurrent neural networks to approximate dynamical systems, then describe a novel algorithm for this task. The algorithm is based on an earlier theoretical result that…
The paper examines the potential of deep learning to support decisions in financial risk management. We develop a deep learning model for predicting whether individual spread traders secure profits from future trades. This task embodies…
We present a neural operator framework for solving inverse scattering problems. A neural operator produces a preliminary indicator function for the scatterer, which, after appropriate rescaling, is used as a regularization parameter within…
We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…
Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman…
Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was…